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This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…

Optimization and Control · Mathematics 2021-04-13 Jingrui Sun , Zhen Wu , Jie Xiong

In this paper, we first prove existence and uniqueness of the solution of a backward doubly stochastic differential equation (BDSDE) and of the related stochastic partial differential equation (SPDE) under monotonicity assumption on the…

Probability · Mathematics 2015-05-19 A. Matoussi , Lambert Piozin , A. Popier

This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some…

Probability · Mathematics 2017-05-03 Shengjun Fan , Lishun Xiao , Yanbin Wang

We deal with backward stochastic differential equations with time delayed generators. In this new type of equations, a generator at time t can depend on the values of a solution in the past, weighted with a time delay function for instance…

Probability · Mathematics 2010-05-27 Łukasz Delong , Peter Imkeller

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a…

Probability · Mathematics 2024-04-17 Guang Yang

We consider the nonlinear Kolmogorov equation posed in a Hilbert space $H$, not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework of weak convergence rates of stochastic wave models. Here,…

Probability · Mathematics 2022-07-06 Javier Castro

The article [HPS] established a monotonicity inequality for the Helmholtz equation and presented applications to shape detection and local uniqueness in inverse boundary problems. The monotonicity inequality states that if two scattering…

Analysis of PDEs · Mathematics 2019-08-02 Bastian Harrach , Valter Pohjola , Mikko Salo

We study invariance and monotonicity properties of Kunita-type stochastic differential equations in $\RR^d$ with delay. Our first result provides sufficient conditions for the invariance of closed subsets of $\RR^d$. Then we present a…

Probability · Mathematics 2012-01-06 Igor Chueshov , Michael Scheutzow

We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic…

Optimization and Control · Mathematics 2015-05-07 Paulwin Graewe , Ulrich Horst , Jinniao Qiu

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…

Optimization and Control · Mathematics 2009-05-12 D. Goreac

We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator $g$ has an iterated-logarithmic uniform continuity in the…

Probability · Mathematics 2023-07-24 Shengjun Fan , Ying Hu , Shanjian Tang

We study linear backward stochastic partial differential equations of parabolic type with special boundary condition that connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability…

Probability · Mathematics 2013-08-01 Nikolai Dokuchaev

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…

Functional Analysis · Mathematics 2021-10-26 Georgy Chargaziya , Alexei Daletskii

Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…

Optimization and Control · Mathematics 2024-03-21 Siqi Qu , Mathias Staudigl

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…

Functional Analysis · Mathematics 2018-05-15 Alexei Daletskii

Given a real and separable Hilbert space H we consider the measure-valued equation \begin{equation*} \int_H\phi(x)\mu_t(dx)- \int_H\phi(x)\mu(dx)= \int_0^t(\int_HK_0\phi(x)\mu_s(dx))ds, \end{equation*} where K_0 is the Kolmogorov…

Analysis of PDEs · Mathematics 2007-07-24 Luigi Manca

This paper investigate a class of multi-dimensional backward stochastic differential equations (BSDEs) with singualr generators exhibiting diagonally quadratic growth and unbounded terminal conditions, thereby extending results in the…

Probability · Mathematics 2025-07-08 Wenbo Wang , Guangyan Jia

In this paper, we study the existence and uniqueness of solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our work is established in infinite dimensional separable…

Probability · Mathematics 2024-07-12 AbdulRahman Al-Hussein

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an…

Optimization and Control · Mathematics 2013-01-15 Wenning Wei

In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro-partial differential equation both with a singular terminal…

Analysis of PDEs · Mathematics 2017-02-03 Alexandre Popier